The ability to read the DNA sequence of an organism's genome has revolutionized biology and biomedical research. Accurate assemblies of sequence data are critical because they provide the foundation for all subsequent work. Using capillary-based sequencing technology, high quality drafts were generated for many genomes. Over the past several years, massively parallel sequencing technologies have lowered sequencing cost by 1000-fold, but the reads from these technologies are shorter and less accurate than the capillary reads, hence harder to assemble, particularly for large genomes. We have recently demonstrated assemblies of massively parallel data that begin to approach the quality of those from capillary data. These assemblies were of genomes for which exceptionally high-quality ('finished') assemblies were already available, and we were thus able not only to rigorously assess the quality of our assemblies, but also to systematically diagnose their defects. Moreover we observe that in almost all cases, defective loci have enough coverage that they could in principle be assembled correctly, provided that the right algorithms were available. On this basis we have proposed a research program to develop computational methods for the creation of assemblies of unprecedented quality: In our first aim we propose to develop methods to achieve high quality draft assemblies of new genomes. Here our objective is to reach and exceed the level of quality that had been achieved using capillary sequencing. In our second aim we will develop methods to achieve ultra high quality assemblies of human genomes. To do this we will leverage the existing human reference sequence and reference sequences of other individuals, including those that we would create. In this way we aim to achieve near-finished quality for regions represented in the reference sequences (essentially via 'resequencing' methods), and at the same time (by de novo methods) capture those regions that are not present in the reference sequences. Our aim is thus to produce the best possible representation of each individual's genome. We note that as costs drop, this is likely to become 'standard of care' for patients. In our third aim, we look beyond existing data, to the next generation of sequencing technologies, to assemble very hard regions using very long and 'strobe' reads. These hard regions include segmental duplications, which are evolutionary hotspots, associated with many diseases, and inaccessible to current methods, except those using very expensive clone-by-clone sequencing. Finally our fourth aim is to make assembly methods accessible to the community. Here our goal is to make it as easy as possible for a range of users (including individual investigators) to match the results achievable by genome assembly experts. In short, through our four aims, we will enable the community to achieve the highest possible assembly quality using the lowest cost data. We thus anticipate that our work will advance a broad range of investigations of importance to biology and human disease.